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REVIEW 3 major objections 5 minor 300 references

Applying the random-phase approximation to a Jastrow-transformed Hamiltonian cuts ground-state energy errors by roughly an order of magnitude and accelerates basis-set convergence, while leaving excitation energies nearly unchanged.

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2026-08-03 01:30 UTC pith:C7QXBYKH

load-bearing objection Genuinely new TC-RPA derivation with useful working equations, but the headline accuracy claim overstates the data and the ground-state benchmark is partly confounded by system-optimized Jastrow factors. the 3 major comments →

arxiv 2607.28845 v1 pith:C7QXBYKH submitted 2026-07-30 physics.chem-ph cond-mat.mtrl-scicond-mat.str-elnucl-th

Transcorrelated Random-Phase Approximation

Abdallah Ammar , Enzo Monino , Anthony Scemama , Emmanuel Giner , Pierre-Fran\c{c}ois Loos This is my paper
classification physics.chem-ph cond-mat.mtrl-scicond-mat.str-elnucl-th
keywords transcorrelated Hamiltonianrandom-phase approximationJastrow factorbasis set convergencecorrelation energyvertical excitation energiesnon-Hermitian quantum chemistrythree-body interactions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tries to show that the slow basis-set convergence long associated with RPA correlation energies can be attacked at the Hamiltonian level: instead of simply enlarging the orbital basis, one first applies a Jastrow similarity transformation that builds the electron-electron cusp into the Hamiltonian, then runs RPA on that non-Hermitian, three-body object. For helium, neon, water, ammonia, methane, and formaldehyde, the resulting TC-dRPA and TC-RPAx methods reach near-asymptotic ground-state energies with much smaller basis sets, and their complete-basis limits sit closer to exact non-relativistic energies—often by nearly an order of magnitude in error. The practical payoff would be accurate correlation energies for small molecules at a fraction of the basis-set cost. The same treatment barely changes vertical excitation energies, which the paper reads as evidence that the ground-state-optimized Jastrow factor does not capture the correlation character of excited states.

Core claim

The central claim is that transcorrelation changes RPA by redefining the effective many-body space, not by adding a small correction. TC orbital energies are already dressed by short-range correlation through the non-symmetric Fock operator, and the particle-hole interaction kernel is built from Jastrow-dressed two-body integrals plus a contraction of the explicit three-body term; the RPA matrix therefore has four independent blocks and separate left and right eigenvectors, and the correlation energy is 1/2 Tr(Omega - A). Numerically, TC-dRPA and TC-RPAx converge with triple- to quadruple-zeta bases while conventional RPA still drifts at quintuple- and sextuple-zeta, and the TC limits are ge

What carries the argument

The key object is the non-Hermitian transcorrelated Hamiltonian, obtained by a similarity transformation with a Jastrow correlation factor, and the effective interaction U-bar = V-bar + sum_k L-bar that fills the A, B, and C blocks of the RPA matrix. The contraction of the three-body term into an effective two-body kernel, together with TC orbital energies from the biorthogonal Fock equation, is what carries short-range correlation into the linear-response problem; the quasiboson approximation then collapses the many-body problem to the finite symplectic eigenvalue problem whose eigenvalues Omega enter the correlation energy formula E = 1/2 Tr(Omega - A).

Load-bearing premise

The load-bearing premise is the quasiboson approximation (Eq. 17)—replacing particle-hole pairs with bosons and correlated ground-state averages with Hartree-Fock ones—which the paper's own text notes can artificially lower ground-state energies (Sections I and II.C), but whose magnitude for the transcorrelated Hamiltonian is never quantified.

What would settle it

Compute TC-dRPA and TC-RPAx correlation energies for a small molecule in a small basis where full configuration interaction is feasible and compare with the exact correlation energy in that basis: if the near-order-of-magnitude improvement over conventional RPA does not survive, the ground-state claim fails. For the excitation claim, re-optimize the Jastrow factor for each excited state and recompute vertical excitation energies: if they still barely move, the ground-state-optimization explanation is wrong.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • TC-dRPA and TC-RPAx offer a practical ground-state route: near-converged energies for small molecules are obtained at triple- or quadruple-zeta quality, avoiding the need for very large basis sets.
  • Because the TC transformation and the RPA approximation do not commute, conventional and transcorrelated RPA have different complete-basis limits; CBS extrapolations of conventional RPA are therefore not the right reference for TC-RPA energies.
  • The ground-state improvement is systematic for TC-dRPA on the molecules tested (errors drop from roughly 44-54 mH to 8-17 mH at the largest basis for water, ammonia, and methane), while TC-RPAx is less uniformly improved and formaldehyde is an outlier.
  • For excited states, TC-RPAx shifts are negligible for water, slightly adverse for ammonia, and helpful for formaldehyde; TC should not be assumed to improve vertical excitation energies.
  • The paper's proposed path to better excitation energies is state-specific or state-averaged Jastrow optimization combined with an improved response kernel, not larger basis sets alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: if Hamiltonian-level dressing is the mechanism, the same biorthogonal RPA derivation could be coupled to better response kernels (Bethe-Salpeter or equation-of-motion coupled-cluster style), combining Jastrow short-range correlation with a more accurate treatment of excitations.
  • Beyond the paper: the small net TC shifts in excitation energies probably hide large canceling changes in absolute ground- and excited-state energies; optimizing the Jastrow factor state by state would test whether that cancellation is the true obstacle.
  • Beyond the paper: the paper's distinction between angular cusp incompleteness (fixed by TC) and radial diffuseness (needed for Rydberg states) predicts a larger TC benefit for valence excitations; the n to pi* case in formaldehyde is a single hint, and a valence-transition benchmark would settle the question.
  • Beyond the paper: because the quasiboson approximation can artificially lower ground-state energies and its size for the TC Hamiltonian is left unquantified, comparing TC-RPA against full configuration interaction correlation energies in small basis sets would separate the Jastrow benefit from the bosonization error.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript extends the random-phase approximation (RPA) to the non-Hermitian transcorrelated (TC) Hamiltonian, which contains explicit three-body interactions generated by a Boys–Handy Jastrow factor. The authors derive TC-RPA equations in a biorthogonal equation-of-motion framework, introduce a quasiboson approximation, and present spin-adapted working equations for two variants: TC-dRPA (direct) and TC-RPAx (with exchange). They apply these methods to ground-state correlation energies and vertical excitation energies of He, Ne, H2O, NH3, CH4, and H2CO. The paper claims that, for ground states, TC-RPA substantially accelerates basis-set convergence and reduces errors by nearly an order of magnitude relative to conventional RPA, while for vertical excitation energies the TC treatment gives only marginal improvements, attributed to the ground-state-optimized Jastrow factor.

Significance. The formal contribution is valuable: extending RPA to a non-Hermitian Hamiltonian with three-body terms is a nontrivial step, and the presented block structure, spin adaptation, and correlation-energy formula are plausible and likely useful for future work in transcorrelated many-body methods. The use of the Quantum Package code and the inclusion of raw data in the Supplementary Materials are positive features. However, the headline numerical claim for ground-state energies is not convincingly established by the benchmarks as presented, because the Jastrow factors are optimized against each system's ground state, and because the H2CO results contradict a systematic improvement. The excited-state results, while negative, are honestly reported and usefully delineate the limitations of the approach.

major comments (3)
  1. [§II.C, Eq. (17)] The central ground-state accuracy claim is confounded by the origin of the Jastrow parameters. Section III.A states that the Boys–Handy parameters were 'optimized at the single-determinant level within a variational Monte Carlo framework' and taken from Refs. 184 and 185. These are ground-state-specific, system-specific fits. The transcorrelated Hamiltonian therefore already contains correlation information tailored to the target ground state, so the improved energies relative to conventional RPA may largely reflect information fed into the Jastrow rather than a superior many-body treatment. The H2CO case at aV5Z directly contradicts the 'nearly an order of magnitude' claim: the dRPA error increases from 53.9 mH to 74.7 mH for TC-dRPA, and the RPAx error from 140.1 mH to 146.3 mH. This outlier is acknowledged in a sentence but is not reconciled with the abstract's sweeping claim. A contr
  2. [§II and Supplementary Materials] The quasiboson approximation is the step that reduces the many-body problem to the finite non-Hermitian RPA matrix of Eq. (19). Replacing particle-hole commutators by delta functions and correlated ground-state expectation values by Hartree–Fock expectation values is already known to be uncontrolled in Hermitian RPA; for a non-Hermitian, biorthogonal TC Hamiltonian, the justification is even weaker. The paper itself notes that this approximation 'can lead to an artificial lowering of the ground-state energy' but does not quantify the effect for the TC Hamiltonian. Since this approximation feeds directly into the correlation energy formula Eq. (32) and into the excitation energies, the numerical results are not yet supported. A concrete test would be to compare TC-RPA against near-exact TC-FCI or TC-selected-CI in a small basis for one of the benchmark systems, which would isolate errors
  3. [§II and Supplementary Materials] The main-text derivation is condensed, with key algebraic steps—the reduction of Eqs. (15)–(16) to the block matrix (19), the eigenvector structure of Eqs. (23)–(24), and the correlation-energy formula (32)—deferred to the Supplementary Materials. As presented, the reader cannot verify these load-bearing equations without reconstructing the derivation. For a methodological paper, this is acceptable only if the supplementary derivation is complete and self-contained; the manuscript should state explicitly that all working equations are derived there and should provide cross-references to the specific supplementary sections. If the supplementary material is not available to the referee or the reader, the equations must be moved into the main text or the paper revised to make the derivation auditable.
minor comments (5)
  1. [Eq. (1)] The summation notation in Eq. (1) is typographically unclear ('N X i N X j,i' and 'k<{i,j}'); please use standard restricted sums over distinct indices.
  2. [Fig. 1] The legend label 'estim exact' should be 'estimated exact' for clarity.
  3. [Fig. 2] For H2CO, the dRPA and TC-dRPA curves are visually close at aV5Z, but the text reports a 53.9 vs 74.7 mH error. Consider adding error annotations or a separate error plot to make the outlier more transparent.
  4. [Tables I–III] The TBE values are CBS estimates, while the RPA values are raw finite-basis results. For a fairer comparison, CBS extrapolated values for the RPA methods (or at least the aV5Z values) should be tabulated alongside the TBEs, especially because basis-set convergence rates differ strongly between methods.
  5. [Abstract] The phrase 'nearly an order of magnitude' is an overstatement given the H2CO results; consider replacing it with 'often substantially' or provide a statistical summary that excludes or flags the outlier.

Circularity Check

0 steps flagged

No significant circularity: the TC-RPA derivation is algebraically self-contained, and the ground-state Jastrow optimization is a benchmark confound rather than a circular reduction.

full rationale

The paper's derivation chain is self-contained at the level of the RPA formalism. The non-Hermitian RPA matrix in Eq. (19) is obtained from the equation-of-motion identities in Eqs. (11a)-(11b) together with the explicitly stated quasiboson approximation, Eq. (17), which replaces fermionic particle-hole commutators by delta functions and correlated ground-state expectation values by Hartree-Fock ones. This is a stated approximation, not a circular substitution of the target result. The correlation energy formula, Eq. (32), E_TC-RPA = (1/2)Tr(Omega - A), is the standard bosonic-diagonalization trace expression and is not identical to any fitted input. The one benchmark-related concern is that the Boys-Handy Jastrow parameters were imported from previous variational Monte Carlo ground-state optimizations (Sec. III.A: 'optimized at the single-determinant level within a variational Monte Carlo framework, were taken from the literature'), and Sec. III.C states the Jastrow 'is optimized exclusively for the ground state.' This is a genuine limitation: the ground-state accuracy claims are not a neutral test of the Jastrow choice. However, it is not a circular derivation. The TC-RPA energy is a nontrivial, nonlinear functional of the TC Hamiltonian, and the paper's own excitation-energy results act as a falsifying control - the same ground-state-optimized Jastrow produces no systematic improvement for excited states, showing that the RPA response is not merely inheriting the Jastrow fit. The self-citations (e.g., Ref. 170) supply the TC Hamiltonian definitions and integral-evaluation details; they are not used as an unverified uniqueness theorem or smuggled ansatz. No equation in the paper reduces a predicted quantity to its input by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 0 invented entities

The method rests on standard bosonization of particle-hole excitations plus a similarity-transformed Hamiltonian. The only fitted inputs are the Jastrow parameters. No new particles, forces, or conserved quantities are introduced. The main unverified assumptions are the validity of the quasiboson replacement for the non-Hermitian TC Hamiltonian, the reality and pairing of its eigenvalues, and the convergence of the three-body quadrature.

free parameters (1)
  • Boys-Handy Jastrow parameters per system = from Ref. 184 (He, Ne) and Ref. 185 (H2O, NH3, CH4, H2CO); values not listed in paper
    The Jastrow factor defines the TC Hamiltonian and therefore every TC-RPA energy. These parameters were optimized at the VMC single-determinant level against ground-state energies of the same systems, so the ground-state benchmark is not parameter-free.
axioms (5)
  • standard math Biorthogonal second-quantization and EOM identities (Eqs. 2-11) hold for the non-Hermitian TC Hamiltonian.
    The whole derivation is built on biorthogonal creation/annihilation algebras and the two EOM identities; these are standard but unproved in the main text.
  • domain assumption The TC Hamiltonian is exactly isospectral to the original electronic Hamiltonian, and the Boys-Handy Jastrow form captures the dominant short-range cusp.
    The paper relies on the TC similarity transformation being isospectral when treated exactly, and on the Boys-Handy form being adequate for the systems studied.
  • domain assumption Quasiboson approximation: particle-hole commutators reduce to delta functions and correlated ground states are replaced by HF determinant expectation values (Eq. 17).
    This approximation is the step that produces the finite RPA matrix Eq. (19) and the correlation energy Eq. (32); the paper acknowledges it can lower ground-state energies artificially.
  • domain assumption The non-Hermitian RPA eigenvalues are real and occur in opposite-sign pairs.
    Section II.B states 'the energies are assumed to be real' and Section II.D asserts the pairing structure 'as a consequence of the symplectic structure' without proof in the main text.
  • domain assumption The on-the-fly quadrature evaluation of three-body TC integrals is sufficiently accurate.
    Section III.A says the three-electron contribution is computed on the fly with a quadrature grid, but no grid-convergence tests are reported.

pith-pipeline@v1.3.0-alltime-deepseek · 24053 in / 15408 out tokens · 180010 ms · 2026-08-03T01:30:41.627087+00:00 · methodology

0 comments
read the original abstract

We extend the random-phase approximation (RPA) to the non-Hermitian transcorrelated (TC) Hamiltonian, which explicitly includes three-body interactions generated by a Jastrow correlation factor. We consider both the direct RPA (dRPA) and RPA with exchange (RPAx). We apply the resulting TC-dRPA and TC-RPAx methods to calculate ground-state correlation energies and vertical excitation energies for atoms (\ce{He} and \ce{Ne}) and small molecules (\ce{H2O}, \ce{NH3}, \ce{CH4}, and \ce{H2CO}). For ground-state correlation energies, the TC treatment substantially improves accuracy and accelerates basis set convergence, reducing errors by nearly an order of magnitude relative to conventional RPA calculations. By contrast, it yields only marginal improvements in vertical excitation energies. We attribute this limited effect to the ground-state optimization of the Jastrow factor, which does not adequately capture the distinct electronic character of excited states. These results establish TC-RPA as an accurate and computationally efficient approach to ground-state energetics, while highlighting the need for state-specific Jastrow optimization to achieve reliable descriptions of excited states.

Figures

Figures reproduced from arXiv: 2607.28845 by Abdallah Ammar, Anthony Scemama, Emmanuel Giner, Enzo Monino, Pierre-Fran\c{c}ois Loos.

Figure 1
Figure 1. Figure 1: FIG. 1. Basis set convergence of the total ground-state energies [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Basis-set convergence of the total ground-state energies (in a.u.) of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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Reference graph

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